Find the function that is finally graphed after the following transformations are applied to the graph of \( y=\sqrt{x} \) in the order listed. (1) Reflect about the \( x \)-axis (2) Shift down 6 units (3) Shift left 2 units \( y=\square \)

To find the function after applying the specified transformations to the graph of \( y = \sqrt{x} \), we will go through each transformation step by step. 1. **Reflect about the \( x \)-axis**: - Reflecting a function about the \( x \)-axis changes the sign of the output. Therefore, the function becomes: \[ y = -\sqrt{x} \] 2. **Shift down 6 units**: - Shifting down means we subtract 6 from the output of the function. Thus, we modify the function to: \[ y = -\sqrt{x} - 6 \] 3. **Shift left 2 units**: - Shifting left involves replacing \( x \) with \( x + 2 \) in the function. Therefore, we update the function to: \[ y = -\sqrt{x + 2} - 6 \] Putting it all together, the final function after all transformations is: \[ y = -\sqrt{x + 2} - 6 \] Thus, the answer is: \[ y = -\sqrt{x + 2} - 6 \]